What is 1/2*ln(t^2(x^2+y^2)) ?

The solution to 1/2*ln(t^2(x^2+y^2)) is ln(t)+1/2 ln(x^2+y^2)

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simplify 1/2*ln(t^2(x^2+y^2))

simplify

\frac{1}{2} \cdot ln (t^{2} (x^{2} + y^{2}))

ln (t) + \frac{1}{2} ln (x^{2} + y^{2})

Solution steps

\frac{1}{2} ln (t^{2} (x^{2} + y^{2}))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

\frac{1}{2} ln (t^{2} (x^{2} + y^{2})) = \frac{1}{2} ln (t^{2}) + \frac{1}{2} ln (x^{2} + y^{2})

= \frac{1}{2} ln (t^{2}) + \frac{1}{2} ln (x^{2} + y^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (t^{2}) = 2 ln (t)

= \frac{1}{2} \cdot 2 ln (t) + \frac{1}{2} ln (x^{2} + y^{2})

\frac{1}{2} \cdot 2 ln (t) = ln (t)

= ln (t) + \frac{1}{2} ln (x^{2} + y^{2})

ln (e^{2} - e^{- 2}) - ln (e - e^{- 1})

ln ∣ x - 1 ∣ - ln ∣ x + 4 ∣

ln (\frac{1}{2 e ^{x^{2}}}) + ln (c)

\frac{1}{4} ln (\frac{2 - 1}{2 + 1})

4 lo g_{10} (x - 6) - 5 lo g_{10} (x)

What is 1/2*ln(t^2(x^2+y^2)) ?
The solution to 1/2*ln(t^2(x^2+y^2)) is ln(t)+1/2 ln(x^2+y^2)